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We study the problem of Bayesian learning in a dynamical system involvingstrategic agents with asymmetric information. In a series of seminal papers inthe literature, this problem has been investigated under a simplifying modelwhere myopically selfish players appear sequentially and act once in the game,based on private noisy observations of the system state and public observationof past players' actions. It has been shown that there exist informationcascades where users discard their private information and mimic the action oftheir predecessor. In this paper, we provide a framework for studying Bayesianlearning dynamics in a more general setting than the one described above. Inparticular, our model incorporates cases where players are non-myopic andstrategically participate for the whole duration of the game, and cases wherean endogenous process selects which subset of players will act at each timeinstance. The proposed framework hinges on a sequential decompositionmethodology for finding structured perfect Bayesian equilibria (PBE) of ageneral class of dynamic games with asymmetric information, where user-specificstates evolve as conditionally independent Markov processes and users makeindependent noisy observations of their states. Using this methodology, westudy a specific dynamic learning model where players make decisions aboutpublic investment based on their estimates of everyone's types. We characterizea set of informational cascades for this problem where learning stops for theteam as a whole. We show that in such cascades, all players' estimates of otherplayers' types freeze even though each individual player asymptotically learnsits own true type.

Decentralized Bayesian learning in dynamic games: A framework for studying informational cascades